Taste Buds - S5-E24
Continuity mistake: Just after Carrie tells Doug that she knows what he has been doing, she storms out of the kitchen. Doug has his hand on a water bottle on the table, then picks it up as he rushes after Carrie. In the next shot of Doug walking into the living room, the water bottle is gone.
Taste Buds - S5-E24
Other mistake: When Doug sits down to eat and Arthur touches his food, Doug says, "That's what my sandwich was missing, a finger with a loose bandaid on it," and pushes Arthur's hand away. When he does this you can see Arthur isn't wearing any bandaids on his hands. (00:00:05 - 00:01:00)
Answer: To answer the question directly. Carrie and Doug do not have a biological child during the show's main run. In season 3 or 4 finale (cant remember which) Carrie has a miscarriage. Later on in the show they find out Carrie has 1 working ovary. Thus reducing the chance of them conceiving. By the final season, they couple agree to adopt from China and go to collect their child in the show's final episode. While on the flight back from China it's revealed that Carrie is once again pregnant. However the last scene of the show is a flash forward showing that Carrie goes full term with that child and they are struggling with both kids.
Ssiscool ★
Adding on to this answer, I read somewhere that producers were afraid of the show having a "before baby" feeling and then an "after baby" feeling. Some fans feel that main characters, or the show in general, decline in quality after a major change. For example, Jesse and Rebecca on "Full House" after they had twin sons, and Daphne on "Frasier" after she married Niles.